Kloosterman sums with multiplicative coefficients

Let f(n)be a multiplicative function satisfying |f(n)|≤1,q(≤N~2)be a positive integer and a be an integer with(a,q)= 1.In this paper,we shall prove that ∑n≤N(n,q)=1f(n)e(an/q)■(1/2)(τ(q)/q)N loglog(6N)+ q~(1/4+ε/2)N~(2/1)(log(6N))~(1/2)+N/(1/2)(loglog(6N)),where n is the multiplicative inverse of n such that nn ≡ 1(mod q),e(x)= exp(2πix),and τ(·)is the divisor function.     

BRIF and CARIF progress

China Institute of Atomic Energy (CIAE) is currently constructing Beijing rare ion beam facility (BRIF) and is proposing China advanced rare ion beam facility (CARIF). This paper is aiming at introducing the progress of BRIF project and the conceptual design CARIF. The ISOL type facility BRIF under construction is composed of a 100 MeV 300 μA proton cyclotron, an ISOL with mass resolution of 20000, and a super-conducting LINAC of 2 MeV/q, and will be commissioned in 2013. CARIF facility proposed is planned to use both ISOL and PF techniques. It is based on a China advanced research reactor CARR that was critical, with ISOL separation of fission fragment, post acceleration to 150 MeV/u, and fragmentation of neutron-rich fission fragment beam like ¹³²Sn. Such unique combination will allow CARIF to deliver beam intensity better than the best world facilities by more than one order of magnitude.     

Michael addition reactions of cyclanones with acrylamides: Producing 2-carbamoylethyl derivatives or ene-lactams

The electron-withdrawing groups (EWGs) in the electrophilic alkenes employed in the Michael addition reaction are almost only CO2R, CN, COR, NO2, and SO2Ph. Although amides (CONR1R2) are also typical electron-withdrawing groups and are of great importance in organic synthesis, they are scarcely em-ployed as the EWGs of the electrophilic alkenes in the Michael addition reaction. In this work, the Mi-chael reactions of acrylamide and its derivatives with cyclanones were successfully carried out in the presence of enough radical inhibitors. The amide groups play a key role in producing the preferred products. The N-substituted acrylamides, including N-monosubstituted and N,N-disubstituted acryla-mides could react with cyclohexanone (CHn) to give the expected 2-carbamoylethyl derivatives; how-ever, acrylamide reacting with cyclohexanone only produced ene-lactam. Cyclanones also have effects on the products, while the ring size of cyclanones influences the reaction yield and the α-substituent decides the ratio of resulting isomeric ene-lactams.     

Arbitrated quantum signature scheme based on reusable key

An arbitrated quantum signature scheme without using entangled states is proposed.In the scheme,by employing a classical hash function and random numbers,the secret keys of signer and receiver can be reused.It is shown that the proposed scheme is secure against several well-known attacks.Specifically,it can stand against the receiver’s disavowal attack.Moreover,compared with previous relevant arbitrated quantum signature schemes,the scheme proposed has the advantage of less transmission complexity.     

The estimate for mean values on prime numbers relative to \frac{4} {p} = \frac{1} {{n_1 }} + \frac{1} {{n_2 }} + \frac{1} {{n_3 }}

If n is a positive integer,let f （n） denote the number of positive integer solutions （n 1,n 2,n 3） of the Diophantine equation 4/n=1/n₁ + 1/n₂ + 1/n₃.For the prime number p,f （p） can be split into f 1 （p） + f 2 （p）,where f i （p） （i=1,2） counts those solutions with exactly i of denominators n 1,n 2,n 3 divisible by p.In this paper,we shall study the estimate for mean values ∑ p相似文献   

BRIF and CARIF progress

China Institute of Atomic Energy (CIAE) is currently constructing Beijing rare ion beam facility (BRIF) and is proposing China advanced rare ion beam facility (CARIF). This paper is aiming at introducing the progress of BRIF project and the con ceptual design CARIF. The ISOL type facility BRIF under construction is composed of a 100 MeV 300 ?A proton cyclotron, an ISOL with mass resolution of 20000, and a super-conducting LINAC of 2 MeV/q, and will be commissioned in 2013. CARIF facility proposed is planned...     

关于F2n中的和集

设F₂为两个元素组成的有限域, F₂ⁿ 为F₂上的n维向量空间. 对于集合A, B ⊆ F₂ⁿ , 它们的和集定义为所有两两互异的和a+b所组成的集合, 其中a∈A, b∈B. Green 和Tao 证明了: 设K > 1,如果A, B ? F₂ⁿ 且|A + B|≤K|A|^1/2|B|^1/2, 则存在一个子空间H?F₂ⁿ 满足
|H|>>exp(-O(√KlogK))|A|
以及x,y∈F₂ⁿ, 使得
|A∩(x+H)|^1/2|B∩(y+H)|^1/2≥1/2K|H|.
本文我们将使用Green 和Tao 的方法并作一些修改, 证明如果|H|>>exp(-O(√K))|A|,
则以上的结论仍然成立.     

On the inverse problem relative to dynamics of the ω function

Let P be the set of prime numbers and P (n) denote the largest prime factor of integer n > 1. Write C3 = {p1p2p3 : pi ∈ P (i = 1, 2, 3), pi = pj (i = j)}, B3 = {p1p2p3 : pi ∈ P (i = 1, 2, 3), p1 = p2 or p1 = p3 or p2 = p3, but not p1 = p2 = p3}. For n = p1p2p3 ∈ C3 ∪ B3, we define the w function by ω(n) = P (p1 + p2)P (p1 + p3)P (p2 + p3). If there is m ∈ S - C3 ∪ B3 such that ω(m) = n, then we call m S-parent of n. We shall prove that there are infinitely many elements of C3 which have enough C3-parents an...     

Why can soil maintain its endless eco-cycle? The relationship between the mechanical properties and ecological attributes of soil

正Dear Editors,Why can soil maintain its endless eco-cycle to sustain the growth of plants?This mystery of nature can be resolved by revealing the relationship between the mechanical properties and ecological attributes of soil.Traditionally,soil science[1-3]is divided into two main categories:pedology and edaphology.In addition,soil mechanics addresses soil from the perspective of mechanics and engineering[4,5].However,no inherent relationship     

On the inverse problem relative to dynamics of the <Emphasis Type="Italic">w</Emphasis> function

Let P be the set of prime numbers and P(n) denote the largest prime factor of integer n > 1. Write